Role of Glucose Risk Factors on Human Breast Cancer: A Nonlinear Dynamical Model Evaluation

Abeer Hamdan Alblowy, Normah Maan () and Sana Abdulkream Alharbi
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Abeer Hamdan Alblowy: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Normah Maan: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Sana Abdulkream Alharbi: Department of Mathematics and Statistics, College of Science, Taibah University, Yanbu 41911, Saudi Arabia

Mathematics, 2022, vol. 10, issue 19, 1-20

Abstract: Understanding of the glucose risk factors-mediated mechanism in human breast cancer remains challenging. In this perception, for the first time, we proposed a complex nonlinear dynamical model that may provide a basic insight into the mechanism of breast cancer for the patient with existing glucose risk factors. The impact of glucose risk factors on the cancer cells’ population is evaluated using the formulated analytical model. The dynamical features of the cancer cells are described by a system of ordinary differential equations. Furthermore, the Routh–Hurwitz stability criterion is used to analyze the dynamical equilibrium of the cells’ population. The occurrence of zero bifurcation as well as two and three of the Jacobian matrix are obtained based on the sums of principal minors of order one. The glucose risk factors are exploited as the bifurcation parameters (acted as necessary and sufficient conditions) to detect the Hopf bifurcation. The presence of excess glucose in the body is found to affect negatively the breast cancer cells’ dynamics, stimulating chaos in the normal and tumor cells and thus drastically deteriorating the efficiency of the human immune system. The theoretical results are validated using the numerical simulations. It is concluded that the present findings may be beneficial for the future breast cancer therapeutic drug delivery and cure.

Keywords: nonlinear dynamical model; breast cancer; glucose risk factor; stability; bifurcation; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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